关于无限分量矢量自旋生成的开Dicke型模型
On the open Dicke-type model generated by an infinite-component vector spin
摘要：
本文考虑一个由无限分量矢量自旋和单模谐振子组成的开放Dicke模型，它们之间通过Jaynes-Cummings型相互作用连接。这种开放量子模型被称为OISD（Open Infinite-component Spin Dicke）模型。利用作用在密度矩阵空间上的超算子研究了OISD Liouvillian的代数结构。一个明确的可逆超算子（准确地说，是一个完全正的保迹映射），将OISD Liouvillian变换成两个独立的Liouvillian之和，一个只由一个缀饰自旋产生，另一个只由一个缀饰谐振子产生。由OISD Liouvillian所产生的时间演化被证明是渐近等价的调整去耦Liouvillian与一些同步的自旋和谐振子的频率所产生的。这种渐近等价性意味着OISD模型的时间演化在任何（微小）耗散的存在下都完全耗散。
英文摘要：
We consider an open Dicke model comprising a single infinite-component vector spin and a single-mode harmonic oscillator which are connected by Jaynes--Cummings-type interaction between them. This open quantum model is referred to as the OISD (Open Infinite-component Spin Dicke) model. The algebraic structure of the OISD Liouvillian is studied in terms of superoperators acting on the space of density matrices. An explicit invertible superoperator (precisely, a completely positive trace-preserving map) is obtained that transforms the OISD Liouvillian into a sum of two independent Liouvillians, one generated by a dressed spin only, the other generated by a dressed harmonic oscillator only. The time evolution generated by the OISD Liouvillian is shown to be asymptotically equivalent to that generated by an adjusted decoupled Liouvillian with some synchronized frequencies of the spin and the harmonic oscillator. This asymptotic equivalence implies that the time evolution of the OISD model dissipates completely in the presence of any (tiny) dissipation.
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